Solve 0.8=0.6^2+0.65^2-c^2/0.6*0.65*2

$$0.8 = \frac { 0.6 ^ { 2 } + 0.65 ^ { 2 } - c ^ { 2 } } { 0.6 \times 0.65 \times 2 }$$

Solve for c

$$c=\frac{\sqrt{1585}}{100}\approx 0.398120585$$

$$c=-\frac{\sqrt{1585}}{100}\approx -0.398120585$$

Steps by Finding Square Root

Calculate 0.6 to the power of 2 and get 0.36.

$$0.8=\frac{0.36+0.65^{2}-c^{2}}{0.6\times 0.65\times 2}$$

Calculate 0.65 to the power of 2 and get 0.4225.

$$0.8=\frac{0.36+0.4225-c^{2}}{0.6\times 0.65\times 2}$$

Add 0.36 and 0.4225 to get 0.7825.

$$0.8=\frac{0.7825-c^{2}}{0.6\times 0.65\times 2}$$

Multiply 0.6 and 0.65 to get 0.39.

$$0.8=\frac{0.7825-c^{2}}{0.39\times 2}$$

Multiply 0.39 and 2 to get 0.78.

$$0.8=\frac{0.7825-c^{2}}{0.78}$$

Divide each term of 0.7825-c^{2} by 0.78 to get \frac{0.7825}{0.78}+\frac{-c^{2}}{0.78}.

$$0.8=\frac{0.7825}{0.78}+\frac{-c^{2}}{0.78}$$

Expand \frac{0.7825}{0.78} by multiplying both numerator and the denominator by 10000.

$$0.8=\frac{7825}{7800}+\frac{-c^{2}}{0.78}$$

Reduce the fraction \frac{7825}{7800} to lowest terms by extracting and canceling out 25.

$$0.8=\frac{313}{312}+\frac{-c^{2}}{0.78}$$

Divide -c^{2} by 0.78 to get -\frac{50}{39}c^{2}.

$$0.8=\frac{313}{312}-\frac{50}{39}c^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{313}{312}-\frac{50}{39}c^{2}=0.8$$

Subtract \frac{313}{312} from both sides.

$$-\frac{50}{39}c^{2}=0.8-\frac{313}{312}$$

Subtract \frac{313}{312} from 0.8 to get -\frac{317}{1560}.

$$-\frac{50}{39}c^{2}=-\frac{317}{1560}$$

Divide both sides by -\frac{50}{39}.

$$c^{2}=\frac{-\frac{317}{1560}}{-\frac{50}{39}}$$

Express \frac{-\frac{317}{1560}}{-\frac{50}{39}} as a single fraction.

$$c^{2}=\frac{-317}{1560\left(-\frac{50}{39}\right)}$$

Multiply 1560 and -\frac{50}{39} to get -2000.

$$c^{2}=\frac{-317}{-2000}$$

Fraction \frac{-317}{-2000} can be simplified to \frac{317}{2000} by removing the negative sign from both the numerator and the denominator.

$$c^{2}=\frac{317}{2000}$$

Take the square root of both sides of the equation.

$$c=\frac{\sqrt{1585}}{100} c=-\frac{\sqrt{1585}}{100}$$

Steps Using the Quadratic Formula

Calculate 0.6 to the power of 2 and get 0.36.

$$0.8=\frac{0.36+0.65^{2}-c^{2}}{0.6\times 0.65\times 2}$$

Calculate 0.65 to the power of 2 and get 0.4225.

$$0.8=\frac{0.36+0.4225-c^{2}}{0.6\times 0.65\times 2}$$

Add 0.36 and 0.4225 to get 0.7825.

$$0.8=\frac{0.7825-c^{2}}{0.6\times 0.65\times 2}$$

Multiply 0.6 and 0.65 to get 0.39.

$$0.8=\frac{0.7825-c^{2}}{0.39\times 2}$$

Multiply 0.39 and 2 to get 0.78.

$$0.8=\frac{0.7825-c^{2}}{0.78}$$

Divide each term of 0.7825-c^{2} by 0.78 to get \frac{0.7825}{0.78}+\frac{-c^{2}}{0.78}.

$$0.8=\frac{0.7825}{0.78}+\frac{-c^{2}}{0.78}$$

Expand \frac{0.7825}{0.78} by multiplying both numerator and the denominator by 10000.

$$0.8=\frac{7825}{7800}+\frac{-c^{2}}{0.78}$$

Reduce the fraction \frac{7825}{7800} to lowest terms by extracting and canceling out 25.

$$0.8=\frac{313}{312}+\frac{-c^{2}}{0.78}$$

Divide -c^{2} by 0.78 to get -\frac{50}{39}c^{2}.

$$0.8=\frac{313}{312}-\frac{50}{39}c^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{313}{312}-\frac{50}{39}c^{2}=0.8$$

Subtract 0.8 from both sides.

$$\frac{313}{312}-\frac{50}{39}c^{2}-0.8=0$$

Subtract 0.8 from \frac{313}{312} to get \frac{317}{1560}.

$$\frac{317}{1560}-\frac{50}{39}c^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-\frac{50}{39}c^{2}+\frac{317}{1560}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{50}{39} for a, 0 for b, and \frac{317}{1560} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-\frac{50}{39}\right)\times \frac{317}{1560}}}{2\left(-\frac{50}{39}\right)}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-\frac{50}{39}\right)\times \frac{317}{1560}}}{2\left(-\frac{50}{39}\right)}$$

Multiply -4 times -\frac{50}{39}.

$$c=\frac{0±\sqrt{\frac{200}{39}\times \frac{317}{1560}}}{2\left(-\frac{50}{39}\right)}$$

Multiply \frac{200}{39} times \frac{317}{1560} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$c=\frac{0±\sqrt{\frac{1585}{1521}}}{2\left(-\frac{50}{39}\right)}$$

Take the square root of \frac{1585}{1521}.

$$c=\frac{0±\frac{\sqrt{1585}}{39}}{2\left(-\frac{50}{39}\right)}$$

Multiply 2 times -\frac{50}{39}.

$$c=\frac{0±\frac{\sqrt{1585}}{39}}{-\frac{100}{39}}$$

Now solve the equation c=\frac{0±\frac{\sqrt{1585}}{39}}{-\frac{100}{39}} when ± is plus.

$$c=-\frac{\sqrt{1585}}{100}$$

Now solve the equation c=\frac{0±\frac{\sqrt{1585}}{39}}{-\frac{100}{39}} when ± is minus.

$$c=\frac{\sqrt{1585}}{100}$$

The equation is now solved.

$$c=-\frac{\sqrt{1585}}{100} c=\frac{\sqrt{1585}}{100}$$